Challenge²
You hear some strange noises behind you and turn around to see three excited scientists. They inform you that they've figured out a way to modify The Portal to take you to a new type of challenging dimension, a system they proudly call 'Challenge2'. You will be able to activate and check out their new technology by clicking the 'Challenge2' button next time you go to use The Portal. Challenge² is a special set of challenges which become permanently unlocked and available for completion after reaching zone 65. These are exact copies of normal challenges, except they don't end at specific zones. Instead, upon completion (through Portal or abandon), each Challenge² grants the player with permanent additional bonuses to attack, health and helium for reaching certain HZE (Highest Zone Ever) milestones. The bonus can only be increased by reaching higher zones in each Challenge²; repeating a single Challenge² to the same zone will not increase it. The total bonus will apply to all your future runs. During a Challenge² run, it is impossible to earn any Helium from any source. This means it is impossible to buy any Wormholes. If a Challenge² is abandoned, similar to standard challenges all the rules will stop applying, and as such, Helium will become obtainable. 15 standard challenges can be unlocked as Challenge²s. These include: *Discipline *Metal *Size *Balance *Meditate *Trimp *Trapper *Electricity *Coordinate *Slow *Nom *Mapology *Toxicity *Watch *Lead In addition, there are two other challenges with completely different rulesets existing purely as a challenge²: *Obliterated *Eradicated Despite having the same rules as standard challenges, you can't complete some challenge related feats (see Achievements) in Challenge²s. Rewards Most Challenge²s give the same rewards for reaching the same zone milestones, with some exceptions. All of the Challenge²s and their following bonuses add to a single separate multiplier, and any additions to this multiplier are additive. The total bonus gained for reaching zone z of a Challenge² using the default reward scheme is \newcommand{\ceil}1{\left \lceil {#1} \right \rceil } \newcommand{\floor}1{\left \lfloor {#1} \right \rfloor } \newcommand{\paren}1{\left ( {#1} \right ) } 5\cdot\paren{\floor{\frac{z}{100}}^2+\floor{\frac{z}{100}} } + \paren{\floor{\frac{z}{100}} + 1}\cdot \floor{\paren{\frac{(z \bmod 100)}{10}}} For every N zones you reach, you get X% more Attack and Health and Y% more Helium Bonus. And every Z zones, you get an increase in further additions to that Challenge's Bonuses. The bonus from previous zones remains the same, but reaching further breakpoints, will give increased bonuses for further zone breakpoints. For example, the default is 1% (X) and 0.1% (Y) every 10 (N) zones, and increases every 100 (Z) zones. This would give a 1%/0.1% boost for reaching 10, 2%/0.2% for reaching 20, up to 10%/1% for reaching 100. However, upon reaching 110, this would be 12% (10+2%)/1.2% (1+0.2%), up to 30% (10+20%)/3% (1+2%) at 200, at which point it increases further to 3%/0.3% per 10 zones past 200. This continues indefinitely, as shown by the table below. The reward formula for every challenge, in general, is: \begin{align*} \text{Reward} &= \begin{cases} f(Z) \cdot m & \text{if } Z < s \left\lfloor 701 / s \right\rfloor + s \\ \left\lfloor \Big( 5f(Z) - 4f(701) - c \Big) \cdot m \right\rceil & \text{if } Z \ge s \left\lfloor 701 / s \right\rfloor + s \end{cases} \\ \\ f(x) &= \frac{t}{2s} \left( g \left\lfloor \frac{x}{t} \right\rfloor ^2 + (2b - g) \left\lfloor \frac{x}{t} \right\rfloor \right) + \left\lfloor \frac{x \bmod t}{s} \right\rfloor \left( b + g \left\lfloor \frac{x}{t} \right\rfloor \right) \\ c &= \frac{4}{s} \left( 701 - s \left\lfloor \frac{701}{s} \right\rfloor \right) \left( b + g \left\lfloor \frac{701}{t} \right\rfloor \right) \\ \\ Z & = \text{highest zone reached in Challenge} ^2 \\ t & = \text{number of zones per reward tier} \\ s & = \text{number of zones per reward step} \\ b & = \text{base reward value per step} \\ g & = \text{reward growth per completed tier} \\ m & = \text{Mesmer mastery bonus: 3 if applicable, 1 if not} \end{align*} Breakdown On the tables below, rewards are formatted as so: X/Y Where X is health and attack % and Y is helium %. Percentages are cumulative, i.e. reach this zone record to have that amount of total bonus from one challenge. Challenge²s are infinite. The tables end arbitrarily. Below is a table of total reward percentage (divide by 10 for Helium) from all 12 default Challenge²s (with the default rewards distribution), therefore it doesn't include Trimp, Trapper, Coordinate, Obliterated or Eradicated. With the Mesmer Mastery, the bonus from the 12 default challenges is tripled. Trivia *The challenges which are not included are Decay, Frugal, Life, Mapocalypse, Crushed, Devastation, Corrupted, Domination, Daily challenges and all Scientist challenges. *The Headstart Mastery is disabled during Challenge² runs. *Completing a Challenge² marks the button with a purple background, which fades to white as its record becomes dwarfed by the highest zone completed. *In patch v4.6, Obliterated was added as a completely new Challenge², having no corresponding Challenge. *In patch v4.10, Eradicated was added as a second new Challenge², also having no corresponding Challenge. Category:Challenges